TY - JOUR AU - Edelman, M. PY - 2013 DA - 2013// TI - Fractional maps as maps with power-law memory JO - Physics VL - 8 ID - Edelman2013 ER - TY - JOUR AU - Rihan, F. A. AU - Baleanu, D. AU - Lakshmanan, S. AU - Rakkiyappan, R. PY - 2014 DA - 2014// TI - On fractional SIRC model with salmonella bacterial infection JO - Abstr. Appl. Anal. VL - 2014 UR - https://doi.org/10.1155/2014/136263 DO - 10.1155/2014/136263 ID - Rihan2014 ER - TY - JOUR AU - Rihan, F. A. AU - Lakshmanan, S. AU - Hashish, A. H. AU - Rakkiyappan, R. AU - Ahmed, E. PY - 2015 DA - 2015// TI - Fractional-order delayed predator–prey systems with Holling type-II functional response JO - Nonlinear Dyn. VL - 80 UR - https://doi.org/10.1007/s11071-015-1905-8 DO - 10.1007/s11071-015-1905-8 ID - Rihan2015 ER - TY - JOUR AU - Nosrati, K. AU - Shafiee, M. PY - 2017 DA - 2017// TI - Dynamic analysis of fractional-order singular Holling type-II predator–prey system JO - Appl. Math. Comput. VL - 313 ID - Nosrati2017 ER - TY - JOUR AU - Padisak, J. PY - 1992 DA - 1992// TI - Seasonal succession of phytoplankton in a large shallow lake (Balaton, Hungary)—a dynamic approach to ecological memory, its possible role and mechanisms JO - J. Ind. Ecol. VL - 80 UR - https://doi.org/10.2307/2261008 DO - 10.2307/2261008 ID - Padisak1992 ER - TY - JOUR AU - Peterson, G. D. PY - 2002 DA - 2002// TI - Contagious disturbance, ecological memory, and the emergence of landscape pattern JO - Ecosystems VL - 5 UR - https://doi.org/10.1007/s10021-001-0077-1 DO - 10.1007/s10021-001-0077-1 ID - Peterson2002 ER - TY - BOOK AU - Kilbas, A. A. AU - Srivastava, H. M. AU - Trujillo, J. J. PY - 2006 DA - 2006// TI - Theory and Applications of Fractional Differential Equations PB - Elsevier CY - Amsterdam ID - Kilbas2006 ER - TY - BOOK AU - Podlubny, I. PY - 1993 DA - 1993// TI - Fractional Differential Equations PB - Academic Press CY - New York ID - Podlubny1993 ER - TY - JOUR AU - Wang, J. L. AU - Li, H. F. PY - 2011 DA - 2011// TI - Surpassing the fractional derivative: concept of the memory-dependent derivative JO - Comput. Math. Appl. VL - 62 UR - https://doi.org/10.1016/j.camwa.2011.04.028 DO - 10.1016/j.camwa.2011.04.028 ID - Wang2011 ER - TY - JOUR AU - Sabatier, J. AU - Agrawal, O. P. AU - Tenreiro Machado, J. A. PY - 2008 DA - 2008// TI - Advances in fractional calculus: theoretical developments and applications in physics and engineering JO - SIAM Rev. VL - 50 ID - Sabatier2008 ER - TY - JOUR AU - Yang, X. J. AU - Srivastava, H. M. AU - Tenreiro Machado, J. A. PY - 2015 DA - 2015// TI - A new fractional derivative without singular kernel: application to the modelling of the steady heat flow JO - Therm. Sci. VL - 20 UR - https://doi.org/10.2298/TSCI151224222Y DO - 10.2298/TSCI151224222Y ID - Yang2015 ER - TY - JOUR AU - Yang, X. J. AU - Gao, F. AU - Tenreiro Machado, J. A. AU - Baleanu, D. PY - 2017 DA - 2017// TI - A new fractional derivative involving the normalized sinc function without singular kernel JO - Eur. Phys. J. Spec. Top. VL - 226 UR - https://doi.org/10.1140/epjst/e2018-00020-2 DO - 10.1140/epjst/e2018-00020-2 ID - Yang2017 ER - TY - JOUR AU - Yang, X. J. AU - Gao, F. AU - Srivastava, H. M. PY - 2018 DA - 2018// TI - A new computational approach for solving nonlinear local fractional PDEs JO - J. Comput. Appl. Math. VL - 339 UR - https://doi.org/10.1016/j.cam.2017.10.007 DO - 10.1016/j.cam.2017.10.007 ID - Yang2018 ER - TY - JOUR AU - Yang, X. J. AU - Gao, F. AU - Ju, Y. AU - Zhou, H. W. PY - 2018 DA - 2018// TI - Fundamental solutions of the general fractional-order diffusion equations JO - Math. Methods Appl. Sci. VL - 41 UR - https://doi.org/10.1002/mma.5341 DO - 10.1002/mma.5341 ID - Yang2018 ER - TY - JOUR AU - Yang, X. J. PY - 2016 DA - 2016// TI - Fractional derivatives of constant and variable orders applied to anomalous relaxation models in heat transfer problems JO - Therm. Sci. VL - 21 UR - https://doi.org/10.2298/TSCI161216326Y DO - 10.2298/TSCI161216326Y ID - Yang2016 ER - TY - JOUR AU - Yang, X. J. AU - Machado, J. A. T. PY - 2017 DA - 2017// TI - A new fractional operator of variable order: application in the description of anomalous diffusion JO - Physica A VL - 481 UR - https://doi.org/10.1016/j.physa.2017.04.054 DO - 10.1016/j.physa.2017.04.054 ID - Yang2017 ER - TY - JOUR AU - Panja, P. PY - 2019 DA - 2019// TI - Stability and dynamics of a fractional-order three-species predator–prey model JO - Theory Biosci. VL - 138 UR - https://doi.org/10.1007/s12064-019-00291-5 DO - 10.1007/s12064-019-00291-5 ID - Panja2019 ER - TY - JOUR AU - Javidi, M. AU - Nyamoradi, N. PY - 2013 DA - 2013// TI - Dynamic analysis of a fractional order prey–predator interaction with harvesting JO - Appl. Math. Model. VL - 37 UR - https://doi.org/10.1016/j.apm.2013.04.024 DO - 10.1016/j.apm.2013.04.024 ID - Javidi2013 ER - TY - JOUR AU - Li, H. L. AU - Zhang, L. AU - Hu, C. AU - Jiang, Y. L. AU - Teng, Z. PY - 2016 DA - 2016// TI - Dynamical analysis of a fractional-order predator–prey model incorporating a prey refuge JO - J. Appl. Math. Comput. VL - 54 UR - https://doi.org/10.1007/s12190-016-1017-8 DO - 10.1007/s12190-016-1017-8 ID - Li2016 ER - TY - JOUR AU - Panja, P. PY - 2019 DA - 2019// TI - Dynamics of a fractional order predator–prey model with intraguild predation JO - Int. J. Model. Simul. VL - 39 UR - https://doi.org/10.1080/02286203.2019.1611311 DO - 10.1080/02286203.2019.1611311 ID - Panja2019 ER - TY - JOUR AU - Vargas-De-LeÓn, C. PY - 2015 DA - 2015// TI - Volterra-type Lyapunov functions for fractional-order epidemic systems JO - Commun. Nonlinear Sci. Numer. Simul. VL - 24 UR - https://doi.org/10.1016/j.cnsns.2014.12.013 DO - 10.1016/j.cnsns.2014.12.013 ID - Vargas-De-LeÓn2015 ER - TY - JOUR AU - Huo, J. AU - Zhao, H. AU - Zhu, L. PY - 2015 DA - 2015// TI - The effect of vaccines on backward bifurcation in a fractional order HIV model JO - Nonlinear Anal., Real World Appl. VL - 26 UR - https://doi.org/10.1016/j.nonrwa.2015.05.014 DO - 10.1016/j.nonrwa.2015.05.014 ID - Huo2015 ER - TY - JOUR AU - Abdelouahab, M. S. AU - Hamri, N. E. AU - Wang, J. PY - 2012 DA - 2012// TI - Hopf bifurcation and chaos in fractional-order modified hybrid optical system JO - Nonlinear Dyn. VL - 69 UR - https://doi.org/10.1007/s11071-011-0263-4 DO - 10.1007/s11071-011-0263-4 ID - Abdelouahab2012 ER - TY - JOUR AU - Moustafa, M. AU - Mohd, M. H. AU - Ismail, A. I. AU - Abdullah, F. A. PY - 2018 DA - 2018// TI - Dynamical analysis of a fractional-order Rosenzweig–MacArthur model incorporating a prey refuge JO - Chaos Solitons Fractals VL - 109 UR - https://doi.org/10.1016/j.chaos.2018.02.008 DO - 10.1016/j.chaos.2018.02.008 ID - Moustafa2018 ER - TY - JOUR AU - Choi, S. K. AU - Kang, B. AU - Koo, N. PY - 2014 DA - 2014// TI - Stability for Caputo fractional differential systems JO - Abstr. Appl. Anal. VL - 2014 ID - Choi2014 ER - TY - JOUR AU - Elsadany, A. AU - Matouk, A. PY - 2015 DA - 2015// TI - Dynamical behaviors of fractional-order Lotka–Volterra predator–prey model and its discretization JO - J. Appl. Math. Comput. VL - 49 UR - https://doi.org/10.1007/s12190-014-0838-6 DO - 10.1007/s12190-014-0838-6 ID - Elsadany2015 ER - TY - JOUR AU - Rihan, F. A. PY - 2003 DA - 2003// TI - Sensitivity analysis of dynamic systems with time lags JO - J. Comput. Appl. Math. VL - 151 UR - https://doi.org/10.1016/S0377-0427(02)00659-3 DO - 10.1016/S0377-0427(02)00659-3 ID - Rihan2003 ER - TY - JOUR AU - Rihan, F. A. AU - Anwar, M. N. PY - 2012 DA - 2012// TI - Qualitative analysis of delayed SIR epidemic model with a saturated incidence rate JO - Int. J. Differ. Equ. VL - 2012 ID - Rihan2012 ER - TY - JOUR AU - Zhang, J. F. PY - 2012 DA - 2012// TI - Bifurcation analysis of a modified Holling–Tanner predator–prey model with time delay JO - Appl. Math. Model. VL - 36 UR - https://doi.org/10.1016/j.apm.2011.07.071 DO - 10.1016/j.apm.2011.07.071 ID - Zhang2012 ER - TY - JOUR AU - Deng, W. AU - Li, C. AU - Lü, J. PY - 2006 DA - 2006// TI - Stability analysis of linear fractional differential system with multiple time delays JO - Nonlinear Dyn. VL - 48 UR - https://doi.org/10.1007/s11071-006-9094-0 DO - 10.1007/s11071-006-9094-0 ID - Deng2006 ER - TY - JOUR AU - Xiao, Z. AU - Xie, X. AU - Xue, Y. PY - 2018 DA - 2018// TI - Stability and bifurcation in a Holling type-II predator–prey model with Allee effect and time delay JO - Adv. Differ. Equ. VL - 2018 UR - https://doi.org/10.1186/s13662-018-1742-4 DO - 10.1186/s13662-018-1742-4 ID - Xiao2018 ER - TY - JOUR AU - Wang, L. AU - Feng, G. PY - 2015 DA - 2015// TI - Stability and Hopf bifurcation for a ratio-dependent predator–prey system with stage structure and time delay JO - Adv. Differ. Equ. VL - 2015 UR - https://doi.org/10.1186/s13662-015-0548-x DO - 10.1186/s13662-015-0548-x ID - Wang2015 ER - TY - JOUR AU - Rihan, F. A. AU - Abdel Rahman, D. H. AU - Lakshmanan, S. AU - Alkhajeh, A. S. PY - 2014 DA - 2014// TI - A time delay model of tumour-immune system interactions: global dynamics, parameter estimation, sensitivity analysis JO - Appl. Math. Comput. VL - 232 ID - Rihan2014 ER - TY - JOUR AU - Yang, R. AU - Zhang, C. AU - Zhang, Y. PY - 2018 DA - 2018// TI - A delayed diffusive predator–prey system with Michaelis–Menten type predator harvesting JO - Int. J. Bifurc. Chaos VL - 28 UR - https://doi.org/10.1142/S0218127418500992 DO - 10.1142/S0218127418500992 ID - Yang2018 ER - TY - JOUR AU - Chinnathambi, R. AU - Rihan, F. A. PY - 2018 DA - 2018// TI - Stability of fractional-order prey–predator system with time-delay and Monod–Haldane functional response JO - Nonlinear Dyn. VL - 92 UR - https://doi.org/10.1007/s11071-018-4151-z DO - 10.1007/s11071-018-4151-z ID - Chinnathambi2018 ER - TY - JOUR AU - Song, P. AU - Zhao, H. AU - Zhang, X. PY - 2016 DA - 2016// TI - Dynamic analysis of a fractional order delayed predator–prey system with harvesting JO - Theory Biosci. VL - 135 UR - https://doi.org/10.1007/s12064-016-0223-0 DO - 10.1007/s12064-016-0223-0 ID - Song2016 ER - TY - JOUR AU - Wang, Z. AU - Wang, X. AU - Li, Y. AU - Huang, X. PY - 2018 DA - 2018// TI - Stability and Hopf bifurcation of fractional-order complex-valued single neuron model with time delay JO - Int. J. Bifurc. Chaos VL - 27 ID - Wang2018 ER - TY - JOUR AU - Yan, Y. AU - Kou, C. PY - 2012 DA - 2012// TI - Stability analysis for a fractional differential model of HIV infection of CD4+ T-cells with time delay JO - Math. Comput. Simul. VL - 82 UR - https://doi.org/10.1016/j.matcom.2012.01.004 DO - 10.1016/j.matcom.2012.01.004 ID - Yan2012 ER - TY - JOUR AU - Yuan, J. AU - Zhao, L. Z. AU - Huang, C. D. AU - Xiao, M. PY - 2019 DA - 2019// TI - Novel results on bifurcation for a fractional-order complex-valued neural network with leakage delay JO - Physica A VL - 514 UR - https://doi.org/10.1016/j.physa.2018.09.138 DO - 10.1016/j.physa.2018.09.138 ID - Yuan2019 ER - TY - JOUR AU - Xu, C. J. AU - Liao, M. X. AU - Li, P. L. AU - Guo, Y. AU - Xiao, Q. M. AU - Yuan, S. PY - 2019 DA - 2019// TI - Influence of multiple time delays on bifurcation of fractional-order neural networks JO - Appl. Math. Comput. VL - 361 ID - Xu2019 ER - TY - JOUR AU - Pyragas, K. PY - 1992 DA - 1992// TI - Continuous control of chaos by self-controlling feedback JO - Phys. Lett. A VL - 170 UR - https://doi.org/10.1016/0375-9601(92)90745-8 DO - 10.1016/0375-9601(92)90745-8 ID - Pyragas1992 ER - TY - JOUR AU - Zhao, H. T. AU - Lin, Y. P. AU - Dai, Y. X. PY - 2011 DA - 2011// TI - Bifurcation analysis and control of chaos for a hybrid ratio-dependent three species food chain JO - Appl. Math. Comput. VL - 218 ID - Zhao2011 ER - TY - JOUR AU - Huang, C. AU - Song, X. AU - Fang, B. AU - Xiao, M. AU - Cao, J. PY - 2018 DA - 2018// TI - Modeling, analysis and bifurcation control of a delayed fractional-order predator–prey model JO - Int. J. Bifurc. Chaos VL - 28 UR - https://doi.org/10.1142/S0218127418501171 DO - 10.1142/S0218127418501171 ID - Huang2018 ER - TY - JOUR AU - Huang, C. AU - Cao, J. AU - Xiao, M. AU - Alsaedi, A. AU - Alsaadi, F. E. PY - 2010 DA - 2010// TI - Controlling bifurcation in a delayed fractional predator–prey system with incommensurate orders JO - Appl. Math. Comput. VL - 293 ID - Huang2010 ER - TY - JOUR AU - Huang, C. D. AU - Li, H. AU - Cao, J. D. PY - 2019 DA - 2019// TI - A novel strategy of bifurcation control for a delayed fractional predator–prey model JO - Appl. Math. Comput. VL - 347 UR - https://doi.org/10.1016/j.cam.2018.07.032 DO - 10.1016/j.cam.2018.07.032 ID - Huang2019 ER - TY - JOUR AU - Zhou, W. G. AU - Huang, C. D. AU - Xiao, M. AU - Cao, J. D. PY - 2019 DA - 2019// TI - Hybrid tactics for bifurcation control in a fractional-order delayed predator–prey model JO - Physica A VL - 515 UR - https://doi.org/10.1016/j.physa.2018.09.185 DO - 10.1016/j.physa.2018.09.185 ID - Zhou2019 ER - TY - JOUR AU - Huang, C. D. AU - Li, T. X. AU - Cai, L. M. AU - Cao, J. D. PY - 2019 DA - 2019// TI - Novel design for bifurcation control in a delayed fractional dual congestion model JO - Phys. Lett. A VL - 383 UR - https://doi.org/10.1016/j.physleta.2018.11.021 DO - 10.1016/j.physleta.2018.11.021 ID - Huang2019 ER - TY - JOUR AU - Xu, C. J. AU - Liao, M. X. AU - Li, P. L. PY - 2019 DA - 2019// TI - Bifurcation control for a fractional-order competition model of Internet with delays JO - Nonlinear Dyn. VL - 95 UR - https://doi.org/10.1007/s11071-018-04758-w DO - 10.1007/s11071-018-04758-w ID - Xu2019 ER - TY - JOUR AU - Xiao, M. AU - Zheng, W. X. AU - Lin, J. X. AU - Jiang, G. P. AU - Zhao, L. D. AU - Cao, J. D. PY - 2017 DA - 2017// TI - Fractional-order PD control at Hopf bifurcations in delayed fractional-order small-world networks JO - J. Franklin Inst. VL - 354 UR - https://doi.org/10.1016/j.jfranklin.2017.09.009 DO - 10.1016/j.jfranklin.2017.09.009 ID - Xiao2017 ER - TY - JOUR AU - Wang, Q. D. AU - Oksasoglu, A. PY - 2005 DA - 2005// TI - Strange attractors in periodically kicked Chua’s circuit JO - Int. J. Bifurc. Chaos VL - 15 UR - https://doi.org/10.1142/S0218127405012028 DO - 10.1142/S0218127405012028 ID - Wang2005 ER - TY - JOUR AU - Xiao, M. AU - Jiang, G. AU - Cao, J. AU - Zheng, W. PY - 2017 DA - 2017// TI - Local bifurcation analysis of a delayed fractional-order dynamic model of dual congestion control algorithms JO - IEEE/CAA J. Autom. Sin. VL - 4 UR - https://doi.org/10.1109/JAS.2016.7510151 DO - 10.1109/JAS.2016.7510151 ID - Xiao2017 ER - TY - JOUR AU - Driessche, P. AU - Watmough, J. PY - 2002 DA - 2002// TI - Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission JO - Math. Biosci. VL - 180 UR - https://doi.org/10.1016/S0025-5564(02)00108-6 DO - 10.1016/S0025-5564(02)00108-6 ID - Driessche2002 ER - TY - BOOK AU - Muth, E. J. PY - 1977 DA - 1977// TI - Transform Methods with Applications to Engineering and Operations Research PB - Prentice Hall CY - New Jersey ID - Muth1977 ER - TY - JOUR AU - Deng, W. H. AU - Li, C. P. PY - 2005 DA - 2005// TI - Synchronization of chaotic fractional Chen system JO - J. Phys. Soc. Jpn. VL - 74 UR - https://doi.org/10.1143/JPSJ.74.1645 DO - 10.1143/JPSJ.74.1645 ID - Deng2005 ER - TY - JOUR AU - Bhalekar, S. AU - Daftardar-Gejji, V. PY - 2011 DA - 2011// TI - A predictor–corrector scheme for solving nonlinear delay differential equations of fractional order JO - J. Fract. Calc. Appl. VL - 4 ID - Bhalekar2011 ER -